We hereby note that as in our system we do not have access to a parameter such as the temperature \(T\) , all the energies and interaction potentials that we compute will be expressed in units of \(kT\) , i.e., \(kT=1\) .
Although mean-field approximation can represent a good first step for a qualitative idea of the interaction in a system, it is a quite
coarse approximation.
Using the mean-field expression for the pair interaction to simulate the evolution of a system in a Monte Carlo simulation does typically not reproduce the expected equilibrium state, which should be consistent with the initial pair correlation \(g(r)\)  [1]}.
